Denmark's Sara Slott Petersen won the silver medal ahead of Ashley Spencer of the United States, with world champion Zuzana Hejnova of the Czech Republic managing only fourth.
With steady rain pouring down at the Olympic stadium, Muhammad shot out of the blocks, rose quickest at the first hurdle and never looked like being overtaken.
She clocked 53.13 seconds to win by a margin of 0.42.
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"The reality of winning is even better than the dream. Olympic champion in front of my name," said Muhammad, runner-up at the 2013 world championship.
The 26-year-old had come to the Rio Games as the fastest woman in the event this year,
Petersen, the European champion, ran 53.55 seconds, and Spencer recorded a personal best of 53.72.
The result underlined U.S. supremacy in the hurdle events, with Kerron Clement winning the men's 400m earlier on Thursday and Brianna Rollins, Nia Ali and Kristi Castlin completing an American podium sweep in the 100m on Wednesday.
(Reporting by Mark Trevelyan, editing by Patrick Johnston)
